186 European Journal of Operational Research 41 (1989) 186-193 North-Holland Theory and Methodology A new heuristic method for the flow shop sequencing problem Marino WIDMER and Alain HERTZ D~partement de Math~matiques, Ecole Polytechnique F~dHale de Lausanne, Chaire de Recherche Op~rationnelle, CH-1015 Lausanne, Switzerland Abstract: A new heuristic method is presented for solving the m-machine, n-job flow shop scheduling problem. This method, named SPIRIT, is composed of two phases: the first finds an initial sequence using an analogy with the travelling salesman problem and the second tries to improve this solution using taboo search techniques. The results of the heuristic are compared with those from other well-known methods. Keywords: Flow shop, schedufing problem, heuristic, makespan, travelling salesman problem, taboo search techniques 1 Introduction During the last 30 years, the flow shop sequenc- ing problem has held the attention of many re- searchers. Since Johnson proposed optimal two- and three-stage production schedules, many heur- istics have been suggested to solve this problem. The flow shop sequencing problem is a produc- tion scheduling problem in which each one of n jobs (tasks, items, etc.) must be processed in the same sequence on each one of m machines (processors, etc.). The processing time of job i on machine j is tq (i = 1..... n; j = 1..... m). If any given job has a processing time equal to zero on one or more machines, the flow shop is called a general flow shop, else it is a pure flow shop. The objective is to find the sequence of jobs mini- mizing the maximum flow time (makespan). Con- way et al. [3] have labelled this problem Received November1987; revised September1988 n/m/F/Fma x (n jobs/m machines/Flow shop/ maximum Flow time). The main assumptions for this problem are the following [1]: - a set of n multiple-operation jobs is availa- ble for processing at time zero (each job requires m operations and each operation requires a differ- ent machine); - the set-up times for the operations are se- quence-independent and are included in the pro- cessing times; - jobs descriptors are known in advance; - m different machines are continuously avail- able; - individual operations are not preemptable. Complete enumeration, branch and bound techniques or integer programming determine the optimal sequence for very small problems, but efficient heuristics are necessary to solve larger ones. In 1954, Johnson presented optimal two- and three-stage production schedules. They are based 0377-2217/89/$3.50 © 1989, ElsevierSciencePublishers B.V. (North-Holland)